A disjointness type property of conditional expectation operators

Beata Randrianantoanina

Colloquium Mathematicae (2005)

  • Volume: 102, Issue: 1, page 9-20
  • ISSN: 0010-1354

Abstract

top
We give a characterization of conditional expectation operators through a disjointness type property similar to band-preserving operators. We say that the operator T:X→ X on a Banach lattice X is semi-band-preserving if and only if for all f, g ∈ X, f ⊥ Tg implies that Tf ⊥ Tg. We prove that when X is a purely atomic Banach lattice, then an operator T on X is a weighted conditional expectation operator if and only if T is semi-band-preserving.

How to cite

top

Beata Randrianantoanina. "A disjointness type property of conditional expectation operators." Colloquium Mathematicae 102.1 (2005): 9-20. <http://eudml.org/doc/283426>.

@article{BeataRandrianantoanina2005,
abstract = {We give a characterization of conditional expectation operators through a disjointness type property similar to band-preserving operators. We say that the operator T:X→ X on a Banach lattice X is semi-band-preserving if and only if for all f, g ∈ X, f ⊥ Tg implies that Tf ⊥ Tg. We prove that when X is a purely atomic Banach lattice, then an operator T on X is a weighted conditional expectation operator if and only if T is semi-band-preserving.},
author = {Beata Randrianantoanina},
journal = {Colloquium Mathematicae},
keywords = {band-preserving; Banach lattice; conditional expectation operator},
language = {eng},
number = {1},
pages = {9-20},
title = {A disjointness type property of conditional expectation operators},
url = {http://eudml.org/doc/283426},
volume = {102},
year = {2005},
}

TY - JOUR
AU - Beata Randrianantoanina
TI - A disjointness type property of conditional expectation operators
JO - Colloquium Mathematicae
PY - 2005
VL - 102
IS - 1
SP - 9
EP - 20
AB - We give a characterization of conditional expectation operators through a disjointness type property similar to band-preserving operators. We say that the operator T:X→ X on a Banach lattice X is semi-band-preserving if and only if for all f, g ∈ X, f ⊥ Tg implies that Tf ⊥ Tg. We prove that when X is a purely atomic Banach lattice, then an operator T on X is a weighted conditional expectation operator if and only if T is semi-band-preserving.
LA - eng
KW - band-preserving; Banach lattice; conditional expectation operator
UR - http://eudml.org/doc/283426
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.